Analyses based on statistical thermodynamics for large difference between thermophilic rhodopsin and xanthorhodopsin in terms of thermostability.

Although the two membrane proteins, thermophilic rhodopsin (TR) and xanthorhodopsin (XR), share a high similarity in amino-acid sequence and an almost indistinguishable three-dimensional structure, TR is much more thermostable than XR. This is counterintuitive also because TR possesses only a smaller number of intramolecular hydrogen bonds (HBs) than XR. Here we investigate physical origins of the remarkable difference between XR and TR in the stability. Our free-energy function (FEF) is improved so that not only the portion within the transmembrane (TM) region but also the extracellular and intracellular portions within the water-immersed (WI) regions can be considered in assessing the stability. The assessment is performed on the basis of the FEF change upon protein folding, which is calculated for the crystal structure of XR or TR. Since the energetics within the TM region is substantially different from that within the WI regions, we determine the TM and WI portions of XR or TR by analyzing the distribution of water molecules using all-atom molecular dynamics simulations. The energetic component of the FEF change consists of a decrease in energy arising from the formation of intramolecular HBs and an increase in energy caused by the break of protein-water HBs referred to as "energetic dehydration penalty." The entropic component is a gain of the translational, configurational entropies of hydrocarbon groups within the lipid bilayer and of water molecules. The entropic component is calculated using the integral equation theory combined with our morphometric approach. The energetic one is estimated by a simple but physically reasonable method. We show that TR is much more stable than XR for the following reasons: The decrease in energy within the TM region is larger, and the energetic dehydration penalty within the WI regions is smaller, leading to higher energetic stabilization, and tighter packing of side chains accompanying the association of seven helices confers higher entropic stabilization on TR.